102 lines
2.7 KiB
C
102 lines
2.7 KiB
C
/*代码来源：https://www.math.wustl.edu/~victor/mfmm/fourier/fft.c*/
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/*华盛顿大学的教学代码*/
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#include <assert.h>
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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//#define q 8 /* 2^q 点，256 */
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//#define N (1<<q) /* N点 FFT, iFFT */
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typedef float real;
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typedef struct
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{
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real Re;
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real Im;
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} complex;
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#ifndef PI
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# define PI 3.14159265358979323846264338327950288
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#endif
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/*为了更好说明分治思想，这里采用递归实现，结束条件为N<=1*/
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void fft(complex *v, int n, complex *tmp)
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{
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if (n > 1) /* N如小于1，直接返回*/
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{
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int k, m;
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complex z, w, *vo, *ve;
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ve = tmp;
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vo = tmp + n / 2;
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for (k = 0; k < n / 2; k++)
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{
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ve[k] = v[2 * k];
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vo[k] = v[2 * k + 1];
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}
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fft(ve, n / 2, v); /* FFT 偶数序列 v[] */
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fft(vo, n / 2, v); /* FFT 偶数序列 v[] */
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for (m = 0; m < n / 2; m++)
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{
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w.Re = cos(2 * PI * m / (double)n);
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w.Im = -sin(2 * PI * m / (double)n);
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z.Re = w.Re * vo[m].Re - w.Im * vo[m].Im; /* Re(w*vo[m]) */
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z.Im = w.Re * vo[m].Im + w.Im * vo[m].Re; /* Im(w*vo[m]) */
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v[ m ].Re = ve[m].Re + z.Re;
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v[ m ].Im = ve[m].Im + z.Im;
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v[m + n / 2].Re = ve[m].Re - z.Re;
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v[m + n / 2].Im = ve[m].Im - z.Im;
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}
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}
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return;
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}
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/*为了更好说明分治思想，这里采用递归实现，结束条件为N<=1*/
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void ifft(complex *v, int n, complex *tmp)
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{
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if (n > 1)
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{
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int k, m;
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complex z, w, *vo, *ve;
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ve = tmp;
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vo = tmp + n / 2;
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for (k = 0; k < n / 2; k++)
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{
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ve[k] = v[2 * k];
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vo[k] = v[2 * k + 1];
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}
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ifft(ve, n / 2, v); /* FFT 偶数序列 v[] */
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ifft(vo, n / 2, v); /* FFT 奇数序列 v[] */
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for (m = 0; m < n / 2; m++)
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{
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w.Re = cos(2 * PI * m / (double)n);
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w.Im = sin(2 * PI * m / (double)n);
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z.Re = w.Re * vo[m].Re - w.Im * vo[m].Im; /* Re(w*vo[m]) */
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z.Im = w.Re * vo[m].Im + w.Im * vo[m].Re; /* Im(w*vo[m]) */
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v[ m ].Re = ve[m].Re + z.Re;
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v[ m ].Im = ve[m].Im + z.Im;
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v[m + n / 2].Re = ve[m].Re - z.Re;
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v[m + n / 2].Im = ve[m].Im - z.Im;
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}
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}
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return;
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}
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void rfft(int32_t *data, int32_t max, int32_t *out, int32_t N)
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{
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complex *v;
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complex *scratch;
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int k;
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v = calloc(N, sizeof(complex));
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scratch = calloc(N, sizeof(complex));
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for (k = 0; k < N; k++)
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{
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v[k].Re = (float)data[k] / max;
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v[k].Im = 0;
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}
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fft(v, N, scratch);
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for (int i = 0; i < N; i++)
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out[i] = sqrt(v[i].Re * v[i].Re + v[i].Im * v[i].Im);
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}
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